


'''simple docstring'''
import math





def    a__			(   lowerCAmelCase__		)       ->      list[int]:
    UpperCAmelCase__     :						List[Any]						=							[]
    UpperCAmelCase__     :						Dict						=							2
    UpperCAmelCase__     :						Optional[Any]						=							int(math.sqrt(lowerCAmelCase__		)		)  # Size of every segment
    UpperCAmelCase__     :						str						=							[True] * (end + 1)
    UpperCAmelCase__     :						Any						=							[]

    while start <= end:
        if temp[start] is True:
            in_prime.append(lowerCAmelCase__		)
            for i in range(start * start    ,   end + 1    ,   lowerCAmelCase__		):
                UpperCAmelCase__     :						Dict						=							False
        start += 1
    prime += in_prime

    UpperCAmelCase__     :						Optional[int]						=							end + 1
    UpperCAmelCase__     :						str						=							min(2 * end    ,   lowerCAmelCase__		)

    while low <= n:
        UpperCAmelCase__     :						List[str]						=							[True] * (high - low + 1)
        for each in in_prime:
            UpperCAmelCase__     :						List[str]						=							math.floor(low / each		) * each
            if t < low:
                t += each

            for j in range(lowerCAmelCase__    ,   high + 1    ,   lowerCAmelCase__		):
                UpperCAmelCase__     :						Union[str, Any]						=							False

        for j in range(len(lowerCAmelCase__		)		):
            if temp[j] is True:
                prime.append(j + low		)

        UpperCAmelCase__     :						Union[str, Any]						=							high + 1
        UpperCAmelCase__     :						str						=							min(high + end    ,   lowerCAmelCase__		)

    return prime







print(sieve(1_0**6))

from __future__ import annotations


def 				lowerCAmelCase__       (			a__    ,     a__ )      ->bool:




  '''simple docstring'''

  _UpperCamelCase           =    get_failure_array(a__ )

  # 2) Step through text searching for pattern
  _UpperCamelCase      ,						_UpperCamelCase           =    0, 0  # index into text, pattern
  while i < len(a__ ):
    if pattern[j] == text[i]:
      if j == (len(a__ ) - 1):
        return True
      j += 1

    # if this is a prefix in our pattern
    # just go back far enough to continue
    elif j > 0:
      _UpperCamelCase           =    failure[j - 1]
      continue
    i += 1
  return False


def 				lowerCAmelCase__       (			a__ )      ->list[int]:




  '''simple docstring'''

  _UpperCamelCase           =    [0]
  _UpperCamelCase           =    0
  _UpperCamelCase           =    1
  while j < len(a__ ):
    if pattern[i] == pattern[j]:
      i += 1
    elif i > 0:
      _UpperCamelCase           =    failure[i - 1]
      continue
    j += 1
    failure.append(a__ )
  return failure


if __name__ == "__main__":
   # Test 1)
   lowerCamelCase__  =					'''abc1abc12'''
   lowerCamelCase__  =					'''alskfjaldsabc1abc1abc12k23adsfabcabc'''
   lowerCamelCase__  =					'''alskfjaldsk23adsfabcabc'''
   assert kmp(pattern, texta) and not kmp(pattern, texta)

   # Test 2)
   lowerCamelCase__  =					'''ABABX'''
   lowerCamelCase__  =					'''ABABZABABYABABX'''
   assert kmp(pattern, text)

   # Test 3)
   lowerCamelCase__  =					'''AAAB'''
   lowerCamelCase__  =					'''ABAAAAAB'''
   assert kmp(pattern, text)

   # Test 4)
   lowerCamelCase__  =					'''abcdabcy'''
   lowerCamelCase__  =					'''abcxabcdabxabcdabcdabcy'''
   assert kmp(pattern, text)

   # Test 5)
   lowerCamelCase__  =					'''aabaabaaa'''
   assert get_failure_array(pattern) == [0, 1, 0, 1, 2, 3, 4, 5, 2]




